This paper considers the two approaches for estimating the parameters specifying the spectral density of the counting process of a stationary point process, namely the frequency domain and the time domain approaches. The relation between the two is clarified; consistency and asymptotic normality of the estimates are established. Finally the special case of a rational spectral density is considered in some detail.
Publié le : 1981-05-14
Classification:
Cumulant,
least square estimation,
maximum likelihood estimation,
periodogram,
point process,
spectral density,
60G10,
62F10,
62M10
@article{1176345465,
author = {Tuan, Pham Dinh},
title = {Estimation of the Spectral Parameters of a Stationary Point Process},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 615-627},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345465}
}
Tuan, Pham Dinh. Estimation of the Spectral Parameters of a Stationary Point Process. Ann. Statist., Tome 9 (1981) no. 1, pp. 615-627. http://gdmltest.u-ga.fr/item/1176345465/